Parisi-Sourlas-like dimensional reduction of quantum gravity in the presence of observers

Abstract

We show that in the presence of disorder induced by random networks of observers measuring covariant quantities (such as scalar curvature) (3+1)-dimensional quantum gravity exhibits an effective dimensional reduction at large spatio-temporal scales, which is analogous to the Parisi-Sourlas phenomenon observed for quantum field theories in random external fields. After averaging over disorder associated with observer networks, statistical properties of the latter determine both the value of gravitational constant and the effective cosmological constant in the model. Focusing on the dynamics of infrared degrees of freedom we find that the upper critical dimension of the effective theory is lifted from D cr = 1+1 to D cr = 3+1 dimensions.